This paper aims at presenting the multiple depot vehicle scheduling problem with heterogeneous fleet and time windows (MDHFVSP-TW). We used a time-space network (TSN) to perform the modeling of MDHFVSP-TW, along with two methodologies to reduce its size and, therefore, its complexity. Along with size reduction methods, a mixed integer programming (MIP) heuristic with variable fixation was presented. Its operation is based on the use of the solution for this problem with relaxed variables as a basis for the removal of arcs from the problem, reducing its size and enabling its resolution in reasonable computational time. Extensive tests were performed for a collection of randomly generated instances. Subsequently, a case study arising from a real instance from a Brazilian city is presented. The computational results showed that the proposed heuristic and size reduction methods obtained good performance, providing high-quality solutions in an adequate computational time.